A folded box is a rectangular prism, so its volume is length times width times height, even without a top. The cut-out square’s side becomes the height. Each base dimension loses a cut length at both ends. Subtracting it only once makes the base too large.
Hints
- Hint 1
For a rectangular prism, volume is length times width times height. When you fold up the cardboard, which length on a cut-out square sets the box’s height?
- Hint 2
Trace one edge of the rectangular base. It runs between two cut-out corners, so it loses at one end and at the other. How much of the original edge remains?
- Hint 3
Find the remaining length of each base edge before multiplying. Multiplying the two base dimensions alone gives area, not volume.
Step-by-step
Find the three box dimensions
Step 1Find the height
No Desmos needed. The cuts tell you the box’s dimensions directly. Folding up the sides makes each cut-out square’s side stand upright, so the box’s height is inches.
- Step 2
Find the base length
On the -inch side, a square is cut from each end. Each sheet dimension loses twice. Subtract both cuts to get the base length:
- Step 3
Find the base width
The -inch side also loses at both ends. Subtract both cuts to get the base width:
- Step 4
Multiply the dimensions
The folded box is a rectangular prism, so its volume is length times width times height. Multiply the dimensions:
That gives the box’s volume in cubic inches; the open top doesn’t change the space inside. Choice D.